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Spline Models for Observational Data (Paperback, New)
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Spline Models for Observational Data (Paperback, New)
Series: CBMS-NSF Regional Conference Series, No 59
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This book serves well as an introduction into the more theoretical
aspects of the use of spline models. It develops a theory and
practice for the estimation of functions from noisy data on
functionals. The simplest example is the estimation of a smooth
curve, given noisy observations on a finite number of its values.
The estimate is a polynomial smoothing spline. By placing this
smoothing problem in the setting of reproducing kernel Hilbert
spaces, a theory is developed which includes univariate smoothing
splines, thin plate splines in d dimensions, splines on the sphere,
additive splines, and interaction splines in a single framework. A
straightforward generalization allows the theory to encompass the
very important area of (Tikhonov) regularization methods for ill
posed inverse problems. Convergence properties, data based
smoothing parameter selection, confidence intervals, and numerical
methods are established which are appropriate to a wide variety of
problems which fall within this framework. Methods for including
side conditions and other prior information in solving ill posed
inverse problems are included. Data which involves samples of
random variables with Gaussian, Poisson, binomial, and other
distributions are treated in a unified optimization context.
Experimental design questions, i.e., which functionals should be
observed, are studied in a general context. Extensions to
distributed parameter system identification problems are made by
considering implicitly defined functionals.
General
Imprint: |
Society For Industrial & Applied Mathematics,U.S.
|
Country of origin: |
United States |
Series: |
CBMS-NSF Regional Conference Series, No 59 |
Release date: |
September 1990 |
First published: |
1990 |
Authors: |
Grace Wahba
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Series editors: |
Ron Rozier
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Dimensions: |
229 x 152 x 11mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
181 |
Edition: |
New |
ISBN-13: |
978-0-89871-244-5 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
0-89871-244-0 |
Barcode: |
9780898712445 |
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